 Hello friends, welcome to yet another session on trigonometry in this session We are going to express all the trigonometric ratios in terms of one ratio so let us say we have to Express cosine theta and all other all other Cosine theta and all other trigonometric ratios like tan theta secant theta cosecant theta and Coat and in theta all this in terms of In terms of sine theta then how should we go about it? Okay, so We will be using the identities which we learned and that is sine square theta Plus cos square theta is equal to one This is the first identity which we are going to use then the other relations like tan theta is tan theta, so we must know all this tan theta is Sine upon cos so using this and other basic Knowledge that secant is one upon cos cosecant is one upon sine and cot is one upon tangent will be able to Express all these five All these five Trigonometric ratios in terms of what? Sine theta let us see how now so from this identity first identity I can write cos square theta is equal to One minus sine square theta just taking sine square theta to the RHS That means cos theta will be nothing but Under root one minus sine square Theta is it so we expressed cos in terms of sine right now This is let's say a Let us now express tan theta. So what is tan theta? We know tan is Sine upon cos so sine theta upon cos theta So hence I can replace cos by whatever we just found out so sine theta upon Under root one minus sine square theta So sine theta is under root one minus sine square theta then third See let us say we now know now know what theta is nothing but one upon tan theta So hence I can just reciprocate this so it is one minus sine square theta upon sine theta Okay, what about? Seek and theta Seek and theta is one upon cos theta So hence it can be written as one upon under root one minus sine square Theta and finally cosecant theta is one upon sine so in this way We could express all the six or all the five other Significatory ratios in terms of sine similarly you can express all all of them in terms of cos as well Right, let us take an example now. Let us say Sine theta is equal to three by five Okay, then what would be cos theta so cos theta will be nothing but one minus sine square theta under root Which is nothing but under root one minus three square by five square Which is nothing but under root five square minus three square by five square, which is nothing but under root 25 minus 9 by 25 Which is equal to? Which is equal to under root 16 by 25 Right, which is equal to then four by five. So I'm only taking the Positive point root of anything is always positive. So four by five. Now, what would be tan theta tan theta will be sine sine theta by cos theta So hence it is three by five by four by five, which is equal to three by four Correct, then what is caught theta again caught theta is one upon tan theta So hence it is four upon three What is secant theta? Secant theta is one upon cos theta which is equal to five upon four and Co secant theta is one upon sine theta Which is equal to five upon three Okay, so hence we could find out all the values of other trigonometric ratios if we know one of them